1. Field of the Invention
The present invention relates to a wavefront dividing type optical integrator; an illumination optical apparatus comprising this optical integrator; and an illumination optical apparatus suitable for exposure apparatus, observation apparatus (microscopes), and the like using this illumination optical apparatus.
2. Related Background Art
In a typical exposure apparatus for making micro devices such as semiconductor device, imaging picking device, liquid crystal display device, and thin film magnetic head, a beam emitted from a light source is incident on a micro fly""s eye lens, and a secondary light source composed of a number of light sources is formed on the image-side focal plane thereof. Beams from the secondary light source are made incident on a condenser lens after being restricted by an aperture stop disposed near the image-side focal plane of the micro fly""s eye lens.
The Beams collected by the condenser lens illuminate, in a superimposing manner, a mask formed with a predetermined pattern. The light transmitted through the pattern of mask forms an image on a photosensitive substrate by way of a projection optical system. Thus, a mask pattern is projected (transferred) onto the photosensitive substrate. The pattern formed in the mask is highly integrated. As a consequence, for accurately transferring this fine pattern onto a photosensitive substrate, it is indispensable that a uniform illuminance distribution be obtained on the photosensitive substrate.
The micro fly""s eye lens is a wavefront dividing type optical integrator composed of a number of micro lenses densely arranged in a matrix. In general, the micro fly""s eye lens is constructed by etching a plane-parallel glass sheet, for example, so as to form a micro lens group. Here, each micro lens constituting the micro fly""s eye lens is smaller than each lens element constituting a fly""s eve lens.
As mentioned above, it is indispensable for a photolithgrahic exposure apparatus for transferring a fine pattern onto a photosensitive substrate to yield a uniform illuminance distribution on the mask and/or on the photosensitive substrate. Reducing the unevenness in illuminance, it has been desired to increase the number of micro lenses micro optical elements constituting the micro fly""s eye lens (micro fly""s eye optical member), i.e., to increase the number of divisions of wavefront.
On the other hand, when making a micro fly""s eye lens by etching and the like, the glass sheet is harder to etch deeply, and the making will be easier if the size of each micro lens is made smaller. However, simply reducing the size of each micro lens is disadvantageous in that illuminance decreases by the amount of diffraction limit with respect to the entrance surface of each micro lens in marginal areas of an illumination field formed on a surface to be irradiated which is optically conjugate with the entrance surface.
It is an object of the present invention to provide a wavefront dividing type optical integrator which can yield a uniform illuminance distribution substantially over the whole illumination field formed thereby even when the size of each micro lens is made smaller so as to set a large number of wavefront divisions; an illumination optical apparatus comprising this optical integrator; and a photolithgrahic exposure apparatus and-observation apparatus comprising this illumination optical apparatus.
The optical integrator in accordance with a first aspect of the present invention is a wavefront dividing type optical integrator, having a number of micro lenses (micro optical elements) arranged two-dimensionally, for forming a number of light sources by dividing a wavefront of an incident beam; each micro lens having a rectangular entrance surface and a rectangular exit surface, and satisfying at least one of the following conditions:
(d1/2)(D1/2)/(xcexxc2x7f)xe2x89xa73.05
(d2/2)(D2/2)/(xcexxc2x7f)xe2x89xa73.05
where f is the focal length of each micro lens, d1 is the length of one side of the entrance surface of each micro lens, d2 is the length of the other side of the entrance surface of each micro lens, D1 is the length of the side of exit surface in each micro lens corresponding to the one side of entrance surface, D2 is the length of the side of exit surface in each micro lens corresponding to the other side of entrance surface, and xc3xa is the wavelength of the incident beam.
The optical integrator may be characterized in that the length d1 of the one side of entrance surface is longer than the length d2 of the other side of entrance surface, and the condition of
(d1/2)(D1/2)/(xcexxc2x7f)xe2x89xa73.05
is satisfied.
The optical integrator in accordance with a second aspect of the present invention is a wavefront dividing type optical integrator, having a number of micro lenses (micro optical elements) arranged two-dimensionally, for forming a number of light sources by dividing a wavefront of an incident beam; each micro lens having a rectangular entrance surface and a circular or regular hexagonal exit surface, and satisfying at least one of the following conditions:
(d1/2)(D/2)/(xcexxc2x7f)xe2x89xa73.05
(d2/2)(D/2)/(xcexxc2x7f)xe2x89xa73.05
where f is the focal length of each micro lens, d1 is the length of one side of the entrance surface of each micro lens, d2 is the length of the other side of the entrance surface of each micro lens, D is the diameter of the circular exit surface or the diameter of a circle circumscribing the regular hexagonal exit surface of each micro lens, and xc3xa is the wavelength of the incident beam.
The optical integrator may be characterized in that the length d1 of the one side of entrance surface is longer than the length d2 of the other side of entrance surface, and the condition of
(d1/2)(D1/2)/(xcexxc2x7f)xe2x89xa73.05
is satisfied.
The optical integrator in accordance with a third aspect of the present invention is a wavefront dividing type optical integrator, having a number of micro lenses (micro optical elements) arranged two-dimensionally, for forming a number of light sources by dividing a wavefront of an incident beam; each micro lens having a circular entrance surface with a diameter of d or a regular hexagonal entrance surface inscribed in a circle having a diameter of d, and satisfying the following condition:
(d1/2)2/(xcexxc2x7f)xe2x89xa73.05
where f is the focal length of each micro lens, and xc3xa is the wavelength of the incident beam.
The illumination optical apparatus in accordance with a fourth aspect of the present invention is an illumination optical apparatus for illuminating a surface to be irradiated according to a beam from a light source, the illumination optical apparatus comprising the optical integrator, disposed in an optical path between the light source and the surface to be irradiated, for forming a number of light sources according to a luminous beam the light source; and a light-guiding optical system, disposed in an optical path between the optical integrator and the surface to be irradiated, for guiding beams from a number of light sources formed by the optical intergrator to the surface to be irradiated.
In the illumination optical apparatus, the light-guiding optical system may comprise a condenser optical system, disposed in the optical path between the optical integrator and the surface to be irradiated, for condensing beams from a number of light sources formed by the optical integrator so as to form an illumination field in a superimposing manner; an image forming optical system, disposed in an optical path between the condenser optical system and the surface to be irradiated, for forming an image of the illumination field near the surface to be irradiated according to a beam from the illumination field; and an aperture stop, disposed in an optical path of the image forming optical system at a position substantially optically conjugate with a position where the light sources are formed, for blocking an unnecessary beam.
In the illumination optical apparatus, each micro lens (micro optical element) in the optical integrator may have at least one refractive surface formed into an aspheric form which is symmetrical about an axis parallel to a reference optical axis in order to attain a substantially uniform illuminance on the surface to be irradiated. If an aspheric surface is introduced into each micro lens element in the optical integrator as such, then the number of parameters in terms of optical designing increases, which makes it easier to yield a desirable design solution, whereby the degree of freedom in design can be improved from the viewpoint of aberration correction in particular. Therefore, in the optical integrator, not only the occurrence of spherical aberration is favorably suppressed, but also the sine condition is substantially satisfied, whereby the occurrence of coma can be suppressed favorably. As a result, unevenness in illumination can favorably be restrained from occurring due to the optical integrator as multiple light source forming member whereby the uniformity in illuminance and the uniformity in numerical aperture can be satisfied at the same time.
In the fourth aspect of the present invention, the above-mentioned effects can be obtained when each micro lens of the optical integrator has at least one aspheric refractive surface even if the condition concerning the entrance surface and exit surface in accordance with the first aspect of the present invention is not satisfied. That is to say, the illumination optical apparatus in accordance with the fourth aspect of the present invention is aimed at satisfying the uniformity in illuminance on the surface to be illuminated and the uniformity in numerical aperture at the same time, and may comprise light source for supplying illumination light, multiple light source forming member for forming a number of light sources according to a beam from the light source, and a condenser optical system for guiding beams from the light sources to the surface to be irradiated or a surface optically conjugate with the surface to be irradiated; wherein the multiple light source forming member has a wavefront dividing type optical integrator comprising a number of micro lens elements, each micro lens element in the wavefront dividing type optical integrator having at least one refractive surface formed into an aspheric form which is symmetrical about an axis parallel to a reference optical axis in order to attain a substantially uniform illuminance on the surface to be irradiated.
In the illumination optical apparatus, the optical integrator may have a number of combining optical systems whose optical axes are respective axes parallel to the reference optical axis, at least one refractive surface formed aspheric being formed into a predetermined aspheric surface in order to favorably restrain coma from occurring in the combining optical systems.
The illumination optical system may be characterized in that it comprises a filter having a predetermined optical transmissivity distribution disposed near the optical integrator on the entrance side thereof in order to correct unevenness in illumination on the surface to be irradiated; and positioning sub-system, connected to the optical integrator and the filter, for positioning the optical integrator and filter with respect to each other. In this case, it is preferred that the positioning means sub-system have an alignment mark formed in the wavefront dividing type optical integrator and an alignment mark formed in the filter.
The illumination optical apparatus may be characterized in that an iris stop adapted to change the size of an opening portion is disposed adjacent the exit surface of the optical integrator.
In the illumination optical apparatus, the optical integrator may have at least two optical element bundles disposed along the reference optical axis with a space therebetween, at least two of the optical element bundles having the aspheric optical surface.
In the illumination optical apparatus, at least two of the optical element bundles may have a number of combining optical systems each comprising at least two micro optical elements corresponding to each other along the axis, all optical surfaces in the combining optical systems being formed into aspheric surfaces having properties identical to each other.
The illumination optical apparatus may comprise positioning sub-system, connected to at least two of the optical element bundles, for positioning at least two of the optical element bundles with respect to each other. In this case, it is preferred that the positioning sub-system have respective alignment marks formed in at least two of optical element bundles. Preferably, a filter having a predetermined optical transmissivity distribution for correcting unevenness in illuminance on the surface to be irradiated is disposed near the wavefront dividing type optical integrator on the entrance side thereof, and the positioning sub-system has an alignment mark formed in the filter in order to position at least two of the optical element bundles and the filter with respect to each other.
In the illumination optical apparatus, the optical integrator may have 1,000 or more axes.
The illumination optical apparatus may have light source image enlarging member, disposed in the optical path between the optical integrator and the light source at or near a position conjugate with the surface to be irradiated, for enlarging the light source image. Employing a configuration having light source image enlarging member as such reduces damages to optical members in the illumination optical apparatus.
In the illumination optical apparatus, the divergent angle of beams by way of the light source image enlarging member may be determined such that no loss in illumination light occurs in the optical integrator.
The illumination optical apparatus may be characterized in that the optical integrator has a plurality of lens surfaces, arranged two-dimensionally, each forming the light source image; the light source image enlarging member enlarges the light source image formed by way of the lens surface; and the divergent angle of the light source image enlarging member is set such that the enlarged light source image is smaller than the lens surface.
In the illumination optical apparatus, the optical integrator may have a plurality of lens surfaces, arranged two-dimensionally, each forming a light source image.
The illumination optical apparatus may be characterized in that a substantially uniform illuminance distribution is formed in a near field of the light source image enlarging member.
The illumination optical apparatus may be characterized in that only one pattern is formed in a far field of the light source image enlarging member.
In the illumination optical apparatus, the far field pattern of the light source image enlarging member may be circular, elliptical, or polygonal.
At a pupil of the illumination optical apparatus, a secondary light source having an optical intensity distribution in which the optical intensity in a pupil center region including an optical axis in a region on the pupil is set lower than that in a region surrounding the pupil center region may be formed.
The illumination optical apparatus may further comprise a diffractive optical element, disposed between the light source and the optical integrator, for controlling a form of the secondary light source formed at the pupil of the illumination optical apparatus.
The illumination optical apparatus may have zeroth-order light blocking member, disposed between the diffractive optical element for controlling the form of the secondary light source and the optical integrator, for blocking zeroth-order light from the diffractive optical element for controlling the form of the secondary light source.
In the illumination optical apparatus, the optical integrator may comprise a plurality of lens surfaces arranged two-dimensionally and an entrance-side cover glass disposed on the entrance side of the plurality of lens surfaces, the entrance-side cover glass being provided with the zeroth-order light blocking member.
In the illumination optical apparatus, the light source image enlarging member may have a diffractive optical element or diffuser.
The illumination optical apparatus may be characterized in that an antireflection film with respect to a wavelength of the illumination light is disposed on a surface of the diffractive optical element or diffuser.
In the illumination optical apparatus, the optical integrator may comprise a plurality of lens surfaces arranged two-dimensionally and an exit-side cover glass disposed on the exit side of the plurality of lens surfaces, the exit-side cover glass being provided with a light-shielding member for blocking light passing through a region different from the plurality of lens surfaces toward the surface to be irradiated.
The illumination optical apparatus may comprise a micro fly""s eye lens (micro fly""s eye optical member) disposed in the optical path between the light source and the surface to be irradiated, comprising a substrate having a surface formed with a plurality of lens surfaces, the lens surfaces of the micro fly""s eye lens being provided with an antireflection film with respect to the illumination light.
The illumination optical apparatus may comprise illuminance distribution correcting member, disposed between the light source and the optical integrator, for controlling respective intensity distributions of Fourier-transformed images of the plurality of light source images independently from each other.
In the illumination optical apparatus, the optical integrator may comprise a plurality of lens surfaces arranged two-dimensionally, an entrance-side cover glass disposed on the entrance side of the plurality of lens surfaces, and an exit-side cover glass disposed on the exit side of the plurality of lens surfaces, the illuminance distribution correcting member being disposed in an optical path between the entrance-side cover glass and the exit-side cover glass.
The illumination optical-apparatus may form an illumination area on the surface to be irradiated, the illuminance region having a form whose length in a predetermined direction differs from that in a direction orthogonal to the predetermined direction.
In the illumination optical apparatus, the antireflection film may have at least one ingredient selected from aluminum fluoride; barium fluoride; calcium fluoride; cerium fluoride; cesium fluoride; erbium fluoride; gadolinium fluoride; hafnium fluoride; lanthanum fluoride; lithium fluoride; magnesium fluoride; sodium fluoride; cryolite; chiolite; neodymium fluoride; lead fluoride; scandium fluoride; strontium fluoride; terbium fluoride; thorium fluoride; yttrium fluoride; ytterbium fluoride; samarium fluoride; dysprosium fluoride; praseodymium fluoride; europium fluoride; holmium fluoride; bismuth fluoride; a fluorine resin comprising at least one material selected from the group consisting of polytetrafluoroethylene, polychlorotrifluoroethylene, polyvinyl fluoride, fluorinated ethylene propylene resin, polyvinylidene fluoride, and polyacetal; aluminum oxide; silicon oxide; germanium oxide; zirconium oxide; titanium oxide; tantalum oxide; niobium oxide; hafnium oxide; cerium oxide; magnesium oxide; neodymium oxide; gadolinium oxide; thorium oxide; yttrium oxide; scandium oxide; lanthanum oxide; praseodymium oxide; zinc oxide; lead oxide; a mixture group and complex compound group comprising at least two materials selected from a group of silicon oxides; a mixture group and complex compound group comprising at least two materials selected from a group of hafnium oxides; and a mixture group and complex compound group comprising at least two materials selected from a group of aluminum oxides.
In the illumination optical apparatus, the light source may supply illumination light having a wavelength of 200 nm or shorter.
In the illumination optical apparatus, the diffractive optical element or micro fly""s eye lens may have silica glass doped with fluorine.
The illumination optical apparatus in accordance with a fifth aspect of the present invention is an illumination optical apparatus for illuminating a surface to be irradiated with a beam from a light source, the apparatus including a plurality of optical elements disposed in an optical path between the light source and the surface to be irradiated, at least one of the optical elements comprising positioning sub-system, provided in the at least one optical element, for optically positioning the at least one optical element.
In the illumination optical apparatus, the positioning sub-system may be disposed outside the optical path between the light source and the surface to be irradiated.
The illumination optical apparatus in accordance with a sixth aspect of the present invention is an illumination optical apparatus for illuminating a surface to be irradiated with illumination light from a light source, the apparatus comprising a micro fly""s eye lens, disposed in an optical path between the light source and the surface to be irradiated, having a substrate with a surface formed with a plurality of lens surfaces; and a condenser optical system, disposed in an optical path between the micro fly""s eye lens and the surface to be irradiated, for guiding a beam from the micro fly""s eye lens to the surface to be irradiated or a surface optically conjugate with the surface to be irradiated, the lens surfaces of the micro fly""s eye lens being provided with an antireflection film with respect to the illumination light. When the antireflection film is provided as such, the efficiency of illumination onto the surface to be irradiated can be improved.
In the illumination optical apparatus, the antireflection film may have at least one ingredient selected from aluminum fluoride; barium fluoride; calcium fluoride; cerium fluoride; cesium fluoride; erbium fluoride; gadolinium fluoride; hafnium fluoride; lanthanum fluoride; lithium fluoride; magnesium fluoride; sodium fluoride; cryolite; chiolite; neodymium fluoride; lead fluoride; scandium fluoride; strontium fluoride; terbium fluoride; thorium fluoride; yttrium fluoride; ytterbium fluoride; samarium fluoride; dysprosium fluoride; praseodymium fluoride; europium fluoride; holmium fluoride; bismuth fluoride; a fluorine resin comprising at least one material selected from the group consisting of polytetrafluoroethylene, polychlorotrifluoroethylene, polyvinyl fluoride, fluorinated ethylene propylene resin, polyvinylidene fluoride, and polyacetal; aluminum oxide; silicon oxide; germanium oxide; zirconium oxide; titanium oxide; tantalum oxide; niobium oxide; hafnium oxide; cerium oxide; magnesium oxide; neodymium oxide; gadolinium oxide; thorium oxide; yttrium oxide; scandium oxide; lanthanum oxide; praseodymium oxide; zincbxide; leadoxide; amixture group and complex compound group comprising at least two materials selected from a group of silicon oxides; a mixture group and complex compound group comprising at least two materials selected from a group of hafnium oxides; and a mixture group and complex compound group comprising at least two materials selected from a group of aluminum oxides.
The illumination optical apparatus in accordance with a seventh aspect of the present invention is an illumination optical apparatus for illuminating a surface to be irradiated with illumination light from a light source, the apparatus comprising a micro fly""s eye lens, disposed in an optical path between the light source and the surface to be irradiated, having a substrate with a surface formed with a plurality of lens surfaces; a condenser optical system, disposed in an optical path between the micro fly""s eye lens and the surface to be irradiated, for guiding a beam beam from the micro fly""s eye lens to the surface to be irradiated or a surface optically conjugate with the surface to be irradiated; and an exit-side protecting member disposed on the exit side of the micro fly""s eye lens and formed from a material transparent to the illumination light, the exit-side protecting member having a light-shielding member, provided in the exit-side protecting member, for blocking light passing through a region of the micro fly""s eye lens different from the plurality of lens surfaces toward the surface to be irradiated. If the light-shielding member is provided as such, so as to block the light passed through the region of micro fly""s eye lens different from the lens surfaces, then image forming performances can be improved.
In the illumination optical apparatus, the optical integrator may comprise an entrance-side cover glass disposed on the entrance side of the micro fly""s eye lens.
The illumination optical apparatus in accordance with an eighth aspect of the present invention is an illumination exposure apparatus, adapted to be combined with a photolithgrahic exposure apparatus comprising a projection optical system by which an image of a pattern on a mask disposed at a first surface is formed on a photosensitive substrate disposed at a second surface, for illuminating the first surface with a beam from a light source, the illumination optical apparatus comprising multiple beam superimposing member, disposed between the light source and the first surface, for dividing the beam from the light source and superimposing thus divided number of beams on an illumination field which is a region on a predetermined surface; and an illumination image forming optical system, disposed between the multiple beam superposing member and the first surface, for forming an image of the illumination field on or near the first surface, the illumination image forming optical system having an aperture stop disposed at a position optically conjugate with a pupil of the projection optical system.
In the illumination optical apparatus, the multiple beam superposing member may divide a wavefront of the beam from the light source.
The exposure apparatus in accordance with a ninth aspect of the present invention is a photolithgrahic exposure apparatus for projecting a pattern of a mask onto a photosensitive substrate, the apparatus comprising the illumination optical apparatus, the surface to be irradiated being set on the photosensitive substrate.
A projection exposure apparatus incorporating the illumination optical apparatus therein can satisfy the uniformity in illuminance in the exposure surface of photosensitive substrate, which is the surface to be irradiated, and the uniformity in numerical aperture. As a result, favorable projection/exposure with a high throughput can be carried out under a favorable exposure condition.
The exposure apparatus in accordance with a tenth aspect of the present invention is a photolithgrahic exposure apparatus for transferring a pattern of a mask disposed on a first surface onto a workpiece disposed on a second surface, the exposure apparatus comprising the illumination optical apparatus for illuminating the first surface; and a projection exposure apparatus, disposed in an optical path between the first and second surfaces, for projecting the pattern of the mask onto the workpiece, the illumination optical apparatus further comprising optical intensity distribution changing member, disposed in the optical path between the light source and the optical integrator, for changing an optical intensity distribution of a beam incident on the optical integrator.
The exposure apparatus in accordance with an eleventh aspect of the present invention is a photolithgrahic exposure apparatus for illuminating a mask formed with a pattern with illumination light in a predetermined wavelength range so as to form an image of the pattern onto a substrate by way of a projection optical system, the exposure apparatus comprising the illumination optical apparatus for supplying the illumination light to the mask.
The exposure apparatus may be characterized in that an illumination area on the mask has a form whose length in a predetermined direction differs from that in a direction orthogonal to the predetermined direction, and exposure is carried out while changing a relative relationship between the mask and the illumination area.
The exposure method in accordance with a twelfth aspect of the present invention is an exposure method in which a mask formed with a pattern is illuminated with illumination light in a predetermined wavelength range so as to form an image of the pattern onto a substrate by way of a projection optical system, wherein the illumination light is supplied to the mask by use of the illumination optical apparatus. When the illumination optical apparatus is used as such, projection/exposure can be carried out under a favorable exposure condition, whereby favorable micro devices (semiconductor device, image pickup device, liquid crystal display picking device, thin film magnetic head, and the like) can be made.
The observation apparatus in accordance with a thirteenth aspect of the present invention is an observation apparatus for forming an image of an object to be observed, the apparatus comprising the illumination optical apparatus for illuminating the object to be observed; and an image forming optical system, disposed between the object to be observed and the image, for forming an image of the object to be observed according to light having traveled by way of the object to be observed.
The illumination optical apparatus in accordance with a fourteenth aspect of the present invention is an illumination optical apparatus for illuminating a surface to be irradiated with illumination light from a light source, the illumination optical apparatus comprising an optical integrator, disposed in an optical path between the light source and the surface to be irradiated, for forming a secondary light source according to a beam from the light source; a condenser optical system, disposed between the optical integrator and the surface to be irradiated, for guiding a beam from the optical integrator to the surface to be irradiated or a surface optically conjugate with the surface to be irradiated; and a diffractive optical element disposed in an optical path between the light source and the surface to be irradiated, a surface of the diffractive optical element being provided with an antireflection film with respect to the illumination light. When the antireflection film is provided as such, the efficiency of illumination onto the surface to be irradiated can be improved.
In the illumination optical apparatus, the antireflection film may have at least one ingredient selected from aluminum fluoride; barium fluoride; calcium fluoride; cerium fluoride; cesium fluoride; erbium fluoride; gadolinium fluoride; hafnium fluoride; lanthanum fluoride; lithium fluoride; magnesium fluoride; sodium fluoride; cryolite; chiolite; neodymium fluoride; lead fluoride; scandium fluoride; strontium fluoride; terbium fluoride; thorium fluoride; yttrium fluoride; ytterbium fluoride; samarium fluoride; dysprosium fluoride; praseodymium fluoride; europium fluoride; holmium fluoride; bismuth fluoride; a fluorine resin comprising at least one material selected from the group consisting of polytetrafluoroethylene, polychlorotrifluoroethylene, polyvinyl fluoride, fluorinated ethylene propylene resin, polyvinylidene fluoride, and polyacetal; aluminum oxide; silicon oxide; germanium oxide; zirconium oxide; titanium oxide; tantalum oxide; niobium oxide; hafnium oxide; cerium oxide; magnesium oxide; neodymium oxide; gadolinium oxide; thorium oxide; yttrium oxide; scandium oxide; lanthanum oxide; praseodymium oxide; zinc oxide; lead oxide; a mixture group and complex compound group comprising at least two materials selected from a group of silicon oxides; a mixture group and complex compound group comprising at least two materials selected from a group of hafnium oxides; and a mixture group and complex compound group comprising at least two materials selected from a group of aluminum oxides.
The present invention will be more fully understood from the detailed description given hereinbelow and the accompanying drawings, which are given byway of illustration only and are not to be considered as limiting the present invention.
Further scope of applicability of the present invention will become apparent from the detailed description given hereinafter. However, it should be understood that the detailed description and specific examples, while indicating preferred embodiments of the invention, are given by way of illustration only, since various changes and modifications within the spirit and scope of the invention will be apparent to those skilled in the art from this detailed description.